In a quantum computer, a quantum algorithm is carried out by applying a series of pulses to a multitude of qubits and coupling elements, such that each pulse sequence realizes a quantum gate. In many superconducting implementations (such as the phase, flux, and transmon qubit based architectures), these control pulses take the form of magnetic flux applied to the qubits. These control pulses are typically generated by room-temperature electronics and are introduced into the cryogenic package via coaxial lines. However, the coaxial line solution is not scalable to the degree required in a useful quantum processor. To achieve the desired level of integration it is necessary to integrate the control circuitry in the qubit cryopackage, and preferably on the same chip as the qubits. Superconducting single-flux-quantum (SFQ) digital technology is a natural choice for implementing integrated control circuitry.
However, there are several difficulties in interfacing SFQ digital control to a quantum-coherent superconducting circuit. First, the shunt resistors that are typically employed in SFQ logic can provide a dissipative environment to the qubits. Second, SFQ pulses generally have a very fast rise-time on the order of few picoseconds and applying them directly to a qubit having an operating frequency of a few GHz will cause significant loss of fidelity by inducing unwanted transitions in the qubit. As an example, for a qubit operating at 10 GHz, the rise-time of the SFQ pulses must be increased to an order of a nanosecond to keep the control adiabatic. Adiabatic control of a qubit with SFQ pulses therefore requires either heavily damping the junctions that generate the control pulses or heavy low-pass filtering of the SFQ pulses. Those skilled in the art of filter design will recognize that any low-pass filter must be at least singly terminated, and therefore filtering the SFQ pulses involves significant damping as well. Since any coupling of the qubit to dissipation sources significantly degrade its coherence, the coupling between the qubit and the control circuitry must be extremely small, and therefore efficiently applying control flux from an SFQ source to a coherent qubit circuit remains a challenge.